A network card rated at 10 Mbps is more than your internet network connection transfer rate. Although you may have a better transfer rate, a greater bandwidth. But, if we are talking about network cards rated at 100 Mbps or 1000 Mbps (1 Gbps) than it is far too much for an internet network connection, your bandwidth assured by your ISP is surely lower thant 100 Mbps.
Your network card does not affect your internet transfer rate unless it's broken. Do you have a guaranteed transfer rate of 44 Mbps? Guaranteed by your ISP that means.
Do you want a better "network gaming machine"? Than, options are simple (and unfortunately a laptop is not easy or cheap to be upgraded): RAM, videocard, processor, motherboard. The discussion could be expanded, but you did not ask for those "outsights". I hope I helped you with the comparison between wan transfer rates and lan transfer rates (wan = internet, lan = a local area network, "hidden" by a router). From my point of view, the network card does not make a difference. Unless it's broken.